MEMS resonator structures offer an attractive alternative to quartz resonators as frequency references for many applications because of their lower cost and reduced form factor.
Temperature and process variations can impact the oscillation frequency of MEMS resonators beyond the tolerance limits of many applications. MEMS resonators are for example used in reference oscillators in RF receiver circuits. The resonance frequency of a MEMS resonator in silicon exhibits a temperature drift of typically −30 ppm/K. For some applications this drift needs to be reduced significantly. For example, when using a MEMS resonator in a GSM reference oscillator the magnitude of drift needs to be below 20 ppm or even 10 ppm over a temperature range of 100K.
The main cause of the temperature dependence of the resonance frequency is the negative temperature coefficient of the elastic modulus exhibited by most of the materials of interest, such as silicon. This results in a reduction in the spring constant at higher temperatures and, consequently, a reduced resonance frequency.
Several solutions have been proposed to correct for the temperature dependence:
Active temperature compensation techniques involve keeping the resonator at a constant temperature by placing the resonator in a temperature controlled feedback loop. In this case, the temperature is measured on, or in close vicinity of the resonator. This temperature is then stabilized by heating the resonator to a preset temperature. This approach is limited by the accuracy of the temperature measurement used to determine the required correction factor.
Passive temperature compensation techniques involve designing the resonator to reduce the dependency of the frequency on temperature. One approach is to combine mono-crystalline silicon with amorphous silicon dioxide (SiO2), since the Young's modulus of SiO2 exhibits an opposite temperature dependency to that of silicon. More generally, this approach involves deposition or growth of layers having a positive temperature coefficient of the elastic modulus to reduce the resulting error. The idea is that the positive coefficient of one material is balanced by the negative coefficient of the other, so that the combined effect is a near-zero temperature coefficient. However, these approaches are sensitive to small variations in the thickness of the deposited layer.
There is therefore a need for improved resonators that exhibit reduced sensitivity to process variations, while preferably simultaneously having a small temperature coefficient (that is, low sensitivity to temperature variations).
US 2008/0143217 discloses a tapered I-shaped bulk acoustic resonator. The resonator has a central rod coupled to two tapered lateral flanges. Process compensation is achieved using the tapered flexural members.